The U.S. military is no longer able to defeat a bloody insurgency in western Iraq or counter al-Qaeda’s rising popularity there, according to newly disclosed details from a classified Marine Corps intelligence report that set off debate in recent months about the military’s mission in Anbar province.

The Marines recently filed an updated version of that assessment that stood by its conclusions and stated that, as of mid-November, the problems in troubled Anbar province have not improved, a senior U.S. intelligence official said yesterday. “The fundamental questions of lack of control, growth of the insurgency and criminality” remain the same, the official said.

WASHINGTON, Nov. 27—A senior American intelligence official said Monday that the Iranian-backed group Hezbollah had been training members of the Mahdi Army, the Iraqi Shiite militia led by Moktada al-Sadr.

The official said that 1,000 to 2,000 fighters from the Mahdi Army and other Shiite militias had been trained by Hezbollah in Lebanon. A small number of Hezbollah operatives have also visited Iraq to help with training, the official said.

Iran has facilitated the link between Hezbollah and the Shiite militias in Iraq, the official said. Syrian officials have also cooperated, though there is debate about whether it has the blessing of the senior leaders in Syria.